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If you are in Class 7 and searching for your ratio chapter, you may not find one. In NCERT's new Ganita Prakash books, ratios have moved to Class 8. This post explains where the topic now sits, what ratio and proportion mean, how to solve the standard problems with worked examples, and the two opposite traps students fall into. Class 7 students who want a head start, and parents checking a syllabus, can both use it.
Where are ratios in the new NCERT books?
Neither part of Class 7 Ganita Prakash has a ratio chapter. The Part 1 contents run from Large Numbers Around Us to Working with Fractions, and the Part 2 contents run from Geometric Twins to Finding the Unknown. The topic opens in Class 8: the Grade 8 Part 1 contents list Chapter 7, "Proportional Reasoning-1", described as exploring "a new way to compare two quantities using daily life situations". Part 2 continues with Proportional Reasoning-2.
Schools using other books may still teach ratios in Class 7, so check your own syllabus. Either way, Class 7 work on fractions is the foundation, because a ratio behaves a lot like a fraction.
What is a ratio?
The Class 8 chapter, Proportional Reasoning-1, starts with a digital image resized in different ways. Some copies look right and some look stretched. A photo 60 units wide and 40 high has a width-to-height ratio of 60 : 40. Read a : b as "for every a units of the first, there are b units of the second".
To simplify a ratio, divide both terms by their HCF. The HCF of 60 and 40 is 20, so 60 : 40 becomes 3 : 2. A photo 90 by 60 also simplifies to 3 : 2 (divide by 30), so it has the same shape. A photo 40 by 20 is 2 : 1, a different shape, which is why it looks stretched.
When are two ratios proportional?
Two ratios are proportional when they are the same in simplest form. The book writes this as a : b :: c : d.
Worked example 1 (from the Class 8 chapter). Are 3 : 4 and 72 : 96 proportional? The HCF of 72 and 96 is 24. 72 ÷ 24 = 3 and 96 ÷ 24 = 4, so 72 : 96 is 3 : 4. Yes.
Worked example 2 (from Proportional Reasoning-2). Idli batter: one mix uses 6 cups of rice to 3 cups of urad dal, another 4 cups to 2. Cross-multiply: 6 × 2 = 12 and 3 × 4 = 12. The products match, so the ratios are proportional, and the batter should taste the same.
Worked example 3. A recipe uses rice and dal in the ratio 2 : 1. How much dal goes with 7 cups of rice? The factor from 2 to 7 is 7 ÷ 2 = 3.5, so dal = 1 × 3.5 = 3.5 cups.
Worked example 4: sharing in a ratio. Share ₹600 between two friends in the ratio 2 : 3. There are 2 + 3 = 5 equal parts, so one part is 600 ÷ 5 = ₹120. The shares are 2 × 120 = ₹240 and 3 × 120 = ₹360. Check: 240 + 360 = 600.
Trap 1: adding when you should multiply
The Class 8 chapter has a neat example. When Neelima is 3, her mother is 30, a ratio of 3 : 30, or 1 : 10. Nine years later they are 12 and 39. That ratio is 12 : 39, or 4 : 13 (divide by 3), not 1 : 10. Both ages went up by the same amount, not by the same factor, so the ratio changed. Watch for "both increased by..." in a question; it usually means the ratio is not kept.
Trap 2: using proportion where it does not apply
The opposite mistake is just as common. Wim Van Dooren and colleagues gave proportional and non-proportional word problems to 1,062 students from Grades 2 to 8 in Not everything is proportional (2005). Students often used proportional methods where they clearly did not fit. These errors grew up to Grade 5 as students got better at proportions. From Grade 6, students more often told the two kinds of situation apart, but even in Grade 8 many proportional errors remained.
A classic example: if 3 towels dry on a line in 3 hours, how long do 6 towels take? If there is room for all of them, still 3 hours. Doubling the towels does not double the drying time. Before you set up a proportion, ask: if one quantity doubles, must the other double too?
A practice routine before Class 8
Simplify five ratios using HCF, from Class 6 and 7 factor work.
Two proportional checks, one by simplest form and one by cross-multiplying.
One sharing problem in a ratio, with a check that the parts add to the total.
One "is it proportional?" question. Decide first, then solve. Write one sentence on why.
Units. The last section of the Class 8 chapter lists conversions such as 1 metre = 3.281 feet, so 2 metres is 6.562 feet. Try one of its exercises too: 600 mL of orange juice to 900 mL of apple juice simplifies to 2 : 3.
If you want to see where proportional reasoning sits among other ideas, the Fermi Concept Library covers every concept in mathematics, each with its own lesson and its place in the map. For the fraction skills underneath ratios, revisit fractions in Class 6, and for where this leads, see direct and inverse proportion in Class 8.
Your next step: measure the width and height of your notebook, write the ratio, simplify it, and check whether a classmate's notebook is proportional.
